CN103279591B - Based on the method for topological optimization design under the solid weight pressure load of extra cell - Google Patents

Based on the method for topological optimization design under the solid weight pressure load of extra cell Download PDF

Info

Publication number
CN103279591B
CN103279591B CN201310143554.2A CN201310143554A CN103279591B CN 103279591 B CN103279591 B CN 103279591B CN 201310143554 A CN201310143554 A CN 201310143554A CN 103279591 B CN103279591 B CN 103279591B
Authority
CN
China
Prior art keywords
extra cell
load
pressure load
design
topological optimization
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired - Fee Related
Application number
CN201310143554.2A
Other languages
Chinese (zh)
Other versions
CN103279591A (en
Inventor
谷小军
朱继宏
孟亮
张亚辉
舒毅潇
张卫红
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Northwestern Polytechnical University
Original Assignee
Northwestern Polytechnical University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Northwestern Polytechnical University filed Critical Northwestern Polytechnical University
Priority to CN201310143554.2A priority Critical patent/CN103279591B/en
Publication of CN103279591A publication Critical patent/CN103279591A/en
Application granted granted Critical
Publication of CN103279591B publication Critical patent/CN103279591B/en
Expired - Fee Related legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Landscapes

  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The invention discloses a kind of based on the method for topological optimization design under the solid weight pressure load of extra cell, for solving the low technical matters of existing method of topological optimization design optimum results performance.Technical scheme introduces extra cell on the surface of contact of solid mass and supporting construction, is loaded on extra cell by solid mass pressure load.Even if in process of topology optimization, borderline material changes like this, but because all nodes of surface of contact are not directly connected with pressure load, but be connected with extra cell, so the size and Orientation of pressure load also can remain unchanged, optimum results performance is high.Application the inventive method is optimized design, topological optimization iterative process need not upgrade pressure load numerical value at every turn, and material and load contact border remain unchanged, and the compliance of optimization rear support structure is 0.0861mJ; The compliance that document 2 method optimizes rear support structure is 0.0967mJ; Prove that the optimum results performance that the inventive method obtains is better.

Description

Based on the method for topological optimization design under the solid weight pressure load of extra cell
Technical field
The present invention relates to a kind of method of topological optimization design, particularly a kind of based on the method for topological optimization design under the solid weight pressure load of extra cell.
Background technology
With reference to Fig. 1 ~ 2.In the field such as Aero-Space, automobile making, structure lightened design under solid weight pressure load is the engineering problem of a quasi-representative, under most topological optimization technology is still confined to solve fixed load, there is the design problem determining border and design domain, namely, in topological optimization iterative process, load does not change; The material boundary of load applying position does not change; Design domain does not change.The difficult point of the design problem on uncertain border is: because the contact area 2 of solid mass and supporting construction may change, thus the total power causing solid mass pressure 1 to be applied in supporting construction changes.The contact area of solid mass and supporting construction
With reference to Fig. 3.Document 1 " TongGaoandWei-hongZhang; Topologyoptimizationofmultiphasematerialstructuresunderd esigndependentpressureloads; InternationalJournalforSimulationandMultidisciplinaryDes ignOptimization.3,297-306 (2009) " discloses the method for topological optimization design under a kind of fixed load compression weight load.Pressure punishment model introduced by document:
p i = x im s Σ ξ = 1 n s x im s S ξ P sw
Wherein, p ifor the pressure on Contact surface element i, n sfor surface in contact number of unit, S ξfor individual unit pressure load active area, s is penalty coefficient, P swfor solid weight pressure load, x imfor the pseudo-density of unit i.In optimizing process after each Optimized Iterative, the pressure load acted on surface in contact unit should recalculate according to corresponding units topology design variable and formula and upgrade finite element model load.
Document 2 " Zhang Weihong, Yang Jungang, Zhu Jihong; Structural topology under pressure load-shape cooperate optimization; Aviation journal; 12nd phase in 2009 " disclose method of topological optimization design under a kind of fixed load.Boundary definition with load contact is non-design domain by document, in topological optimization iterative process, owing to remaining unchanged, so pressure load also can remain unchanged with the material (non-design domain) of compression weight load contact.
Although method disclosed in document 1 can realize the topology optimization design under solid weight pressure load, but its method is too complicated, each topological optimization iteration all will recalculate the pressure load numerical value of effect each unit on the contact surface, affects Optimized Iterative efficiency.Although method disclosed in document 2 can keep the size and Orientation of pressure load constant in topological optimization iterative process, but due to the material contacted with pressure load is defined in order to non-design domain, the structure causing this Topological optimization model to be designed and the material of load contact can not be removed, design domain reduces, design constraint increases, and optimum results performance reduces.
Summary of the invention
In order to overcome the low deficiency of existing method of topological optimization design optimum results performance, the invention provides a kind of based on the method for topological optimization design under the solid weight pressure load of extra cell.The method introduces extra cell on the surface of contact of solid mass and supporting construction, Young modulus 1-2 the order of magnitude larger than the Young modulus of structure of extra cell, the borderline unit contacted with solid mass pressure load is connected with extra cell, solid mass pressure load is not directly loaded in material boundary, but is loaded on extra cell.Even if borderline material changes in process of topology optimization like this, but be not directly connected with pressure load due to all nodes of surface of contact, but be connected with extra cell, so the size and Orientation of pressure load also can remain unchanged.This method can realize the topology optimization design requirement under solid weight pressure load, size and the aspect of maintenance pressure load are constant, but do not upgrade load value in each iteration, affect iteration efficiency, also do not introduce non-design domain, limiting material border is constant, optimum results performance is high.
The technical solution adopted for the present invention to solve the technical problems is: a kind of based on the method for topological optimization design under the solid weight pressure load of extra cell, is characterized in comprising the following steps:
A () sets up finite element model by the cad model of structure; The surface of contact 2 of solid mass and supporting construction defines extra cell, extra cell Young modulus 1-2 the order of magnitude larger than structured material Young modulus; Definition load, is loaded into solid mass pressure 1 load on extra cell.
B () building topology Optimized model is:
findX=(x 1,x 2,…,x n)
minΦ(X)
s.t.KU=F
G j ( X ) - G - j ≤ 0 , j = 1 , . . . , J
Wherein, X is the pseudo-intensity vector of unit in design domain; N is design variable number; The objective function that Φ (X) is topological optimization; K is finite element model global stiffness matrix; F is node equivalent load vectors; U is node global displacement vector; G j(X) be a jth constraint function; for the upper limit of a jth constraint function; J is the quantity of constraint.
C model is carried out a finite element analysis by (); By optimizing sensitivity analysis, try to achieve the sensitivity of objective function and constraint condition, choose certain optimized algorithm and be optimized design, be optimized result.
The invention has the beneficial effects as follows: because the method introduces extra cell on the surface of contact of solid mass and supporting construction, Young modulus 1-2 the order of magnitude larger than the Young modulus of structure of extra cell, the borderline unit contacted with solid mass pressure load is connected with extra cell, solid mass pressure load is not directly loaded in material boundary, but is loaded on extra cell.Even if borderline material changes in process of topology optimization like this, but be not directly connected with pressure load due to all nodes of surface of contact, but be connected with extra cell, so the size and Orientation of pressure load also can remain unchanged.This method can realize the topology optimization design requirement under solid weight pressure load, size and the aspect of maintenance pressure load are constant, but do not upgrade load value in each iteration, affect iteration efficiency, also do not introduce non-design domain, limiting material border is constant, optimum results performance is high.Application the inventive method is optimized design, topological optimization iterative process need not upgrade pressure load numerical value at every turn, and material and load contact border remain unchanged, and the compliance of optimization rear support structure is 0.0861mJ; And the method applied in document 1, then need to upgrade load value in each iterative process, load contact face is defined as non-design domain by the method in application document 2, and the compliance optimizing rear support structure is 0.0967mJ; The optimum results performance that the method applied in the present invention obtains is better.
Accompanying drawing explanation
Fig. 1 is the structural representation of solid weight pressure load in background technology.
Fig. 2 is solid weight pressure load distribution schematic diagram in background technology.
Fig. 3 is the method schematic diagram solving the use of this problem in background technology list of references 2.
Fig. 4 is the supporting construction schematic diagram of using method of the present invention.
Fig. 5 is the stress model of moulded dimension schematic diagram the inventive method of specific embodiment.
Fig. 6 is the topology optimization design result of specific embodiment application the inventive method.
Fig. 7 is the topology optimization design result of list of references 2 method in specific embodiment application background technology.
In figure, 1-solid mass pressure; The surface of contact of 2-solid mass and supporting construction.
Embodiment
With reference to Fig. 4 ~ 7.For two-dimensional solid compression weight load structure, the present invention is described.Two dimension support physical dimension is long 500mm, high 300mm, and thickness is 1mm, and its Young modulus is 2.1 × 10 5mpa, Poisson ratio is 0.3.Weight quality is 10kg, entirely fixes bottom supporting construction.Design supporting construction, make its rigidity maximum, material usage volume fraction is 30% to the maximum.Method step is as follows:
(a) finite element modeling.
Finite element model is set up: the setting grid length of side is 10mm, grid division by the cad model of structure.Definition load: because weight quality is 10kg, get gravity acceleration g=9.8m/s 2, according to weight and supporting structure contact area, then pressure is 0.196Mpa.Definition boundary condition: whole for supporting construction bottom node degree of freedom is fixed.The surface of contact 2 of solid mass and supporting construction defines extra cell, and extra cell Young modulus is 2.1 × 10 7mpa; Definition load: solid mass pressure 1 load is loaded on extra cell.
B () building topology Optimized model is
findX=(x 1,x 2,…,x n)
minΦ(X)
s.t.KU=F
G(X)-0.3≤0
Wherein, X is design variable---the pseudo-intensity vector of the unit in design domain; N is design variable number; Φ (X) is objective function, is the rigidity of supporting construction in the present embodiment; K is finite element model global stiffness matrix; F is node equivalent load vectors; U is node global displacement vector; The volume fraction that G (X) is finite element model.
(c) finite element analysis and Optimization Solution.
By finite element soft Ansys, model is carried out a finite element analysis; Sensitivity analysis is optimized again by structure optimization platform Boss-Quattro, try to achieve the sensitivity of objective function and constraint condition, choose gradient optimal method GCMMA(GloballyConvergentMethodofMovingAsymptotes) optimized algorithm is optimized design, and be optimized result.
As can be seen from Fig. 6 and Fig. 7 optimum results, carry out the topology optimization design under solid weight pressure load by the inventive method, the borderline unit of load contact can be removed in topological optimization iterative process, and does not change the size of load.Compared with document 1 method, the inventive method does not need to upgrade pressure load in each topological optimization iterative process, decreases topological optimization iteration time; By contrasting can find out with document 2 method, the optimum results compliance that the inventive method obtains is 0.0861mJ, and the optimum results compliance that documents 2 method obtains is 0.0967mJ; The optimum results performance that the method applied in the present invention obtains is better.

Claims (1)

1., based on the method for topological optimization design under the solid weight pressure load of extra cell, it is characterized in that comprising the following steps:
A () sets up finite element model by the cad model of structure; The surface of contact (2) of solid mass and supporting construction defines extra cell, extra cell Young modulus 1-2 the order of magnitude larger than structured material Young modulus; Definition load, is loaded on extra cell by solid mass pressure (1) load;
B () building topology Optimized model is:
findX=(x 1,x 2,…,x n)
minΦ(X)
s.t.KU=F
G j ( X ) - G ‾ j ≤ 0 , j = 1 , ... , J
In formula, X is the pseudo-intensity vector of unit in design domain; N is design variable number; The objective function that Φ (X) is topological optimization; K is finite element model global stiffness matrix; F is node equivalent load vectors; U is node global displacement vector; G j(X) be a jth constraint function; for the upper limit of a jth constraint function; J is the quantity of constraint;
C model is carried out a finite element analysis by finite element soft Ansys by (); Be optimized sensitivity analysis by structure optimization platform Boss-Quattro again, try to achieve the sensitivity of objective function and constraint condition, choose gradient optimal method GCMMA and be optimized design, be optimized result.
CN201310143554.2A 2013-04-24 2013-04-24 Based on the method for topological optimization design under the solid weight pressure load of extra cell Expired - Fee Related CN103279591B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201310143554.2A CN103279591B (en) 2013-04-24 2013-04-24 Based on the method for topological optimization design under the solid weight pressure load of extra cell

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201310143554.2A CN103279591B (en) 2013-04-24 2013-04-24 Based on the method for topological optimization design under the solid weight pressure load of extra cell

Publications (2)

Publication Number Publication Date
CN103279591A CN103279591A (en) 2013-09-04
CN103279591B true CN103279591B (en) 2016-01-20

Family

ID=49062108

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201310143554.2A Expired - Fee Related CN103279591B (en) 2013-04-24 2013-04-24 Based on the method for topological optimization design under the solid weight pressure load of extra cell

Country Status (1)

Country Link
CN (1) CN103279591B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106096172A (en) * 2016-06-22 2016-11-09 西北工业大学 Load controlled delivery structural topological optimization method

Families Citing this family (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2015111352A (en) * 2013-12-06 2015-06-18 三菱重工業株式会社 Structure analysis method
CN106202786B (en) * 2016-07-19 2019-05-21 大连理工大学 A kind of filtered variable design method about big L/D ratio cylindrical shell structure topological optimization
CN107357974B (en) * 2017-03-31 2020-07-31 华侨大学 Non-uniform fiber reinforced composite material distribution optimization design method
CN109760309B (en) * 2019-01-16 2021-03-16 北京工业大学 Manufacturing method of ankle-foot orthosis based on 3D printing technology

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102117357A (en) * 2010-12-14 2011-07-06 深圳市大族激光科技股份有限公司 Weight-reducing optimal design method for parts of PCB (printed circuit board) numerical control drilling and milling machine

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102117357A (en) * 2010-12-14 2011-07-06 深圳市大族激光科技股份有限公司 Weight-reducing optimal design method for parts of PCB (printed circuit board) numerical control drilling and milling machine

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
多相材料结构拓扑优化:体积约束还是质量约束;高彤等;《力学学报》;20110331;第43卷(第2期);全文 *
静力载荷和随机激励下结构拓扑优化设计;张桥,张卫红,朱继宏;《中国计算力学大会2010暨第八届南方计算力学学术会议》;20101231;全文 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106096172A (en) * 2016-06-22 2016-11-09 西北工业大学 Load controlled delivery structural topological optimization method
CN106096172B (en) * 2016-06-22 2019-12-20 西北工业大学 Topological optimization method of load-controllable transfer structure

Also Published As

Publication number Publication date
CN103279591A (en) 2013-09-04

Similar Documents

Publication Publication Date Title
CN103279591B (en) Based on the method for topological optimization design under the solid weight pressure load of extra cell
Amir et al. Approximate reanalysis in topology optimization
CN110008512B (en) Negative Poisson ratio lattice structure topology optimization method considering bearing characteristics
Dubinski et al. GOTPM: a parallel hybrid particle-mesh treecode
CN103217906B (en) Based on the method for topological optimization design under the solid weight pressure load of equation of constraint
CN104765922A (en) Method for topological optimization design of cantilever beam structure based on shape-preserved constraints
CN113191040A (en) Single-material structure topology optimization method and system considering structure stability
CN106844917A (en) A kind of lathe base method of topological optimization design based on support reaction Variance Constraints
CN105868489A (en) Accurate deformation constraint based cantilever beam structure topological optimization design method
CN106294975B (en) A kind of girder structure free vibration analysis method based on reduced-order model
CN103294857A (en) Topological optimization method of constrained damping plate with frequency response displacement as optimization objective
CN114756934B (en) Three-dimensional multi-scale metamaterial structure optimization design method
Bai et al. An improved numerically-stable equivalent static loads (ESLs) algorithm based on energy-scaling ratio for stiffness topology optimization under crash loads
Li et al. A peridynamic model for the nonlinear static analysis of truss and tensegrity structures
CN106295028A (en) A kind of partial structurtes dynamic modeling method and device
CN106354954B (en) A kind of three-dimensional mechanical Modal Analysis analogy method based on hierarchical basis functions
CN103853921A (en) Method for predicting flow-induced vibration characteristic of large-deformation super-elastic structure
CN102521463A (en) Method for improving numerical reservoir simulation efficiency by optimizing behaviors of Cache
CN103065015A (en) Internal force path geometrical morphology based low-carbon material-saving bearing structure design method
CN109948253B (en) GPU acceleration method for thin-plate meshless Galerkin structure modal analysis
CN116842799A (en) Continuous multi-material structure topology optimization method for carrier lightweight design
CN107345409A (en) Calculation method for elastic foundation upper beam
CN103324803A (en) Modeling method and device of spinning machine
CN113255196B (en) Grid optimization method, grid generator and storage medium
Nguyen Computational homogenization of cellular materials capturing micro-buckling, macro-localization and size effects

Legal Events

Date Code Title Description
C06 Publication
PB01 Publication
C10 Entry into substantive examination
SE01 Entry into force of request for substantive examination
C14 Grant of patent or utility model
GR01 Patent grant
CF01 Termination of patent right due to non-payment of annual fee
CF01 Termination of patent right due to non-payment of annual fee

Granted publication date: 20160120